The content and principles underpinning the 2014 mathematics curriculum reflect those found in high performing education systems internationally, particularly those of east and south-east Asian countries such as Singapore, Japan, South Korea and China. Although there are many differences between the education systems of England and those of east and south-east Asia, we can learn from the ‘mastery’ approach to teaching commonly followed in these countries. Stopsley has adopted the principles and features which characterise this methodology to address the three aims of the National Curriculum – Fluency – Reasoning – Problem Solving.

Lesson Design

• Whole class together – we teach mathematics to whole classes and all children are encouraged to believe that by working hard they can succeed in maths. Lessons are planned based on formative assessment of what is already known and we include all children in learning mathematical concepts. At the planning stage, teachers consider what scaffolding may be required for children who may struggle to grasp concepts in the lesson and suitable challenge questions for those who may grasp the concepts rapidly. Decisions are not made about who these children may be prior to the lesson.

• Longer and deeper – in order to address the aims of the National Curriculum, our planning has been adjusted to allow longer time to be spent on topics. Each lesson focuses on one key conceptual idea and connections are made across mathematical topics. It may appear that the pace of the lesson is slower, but progress and understanding is enhanced. Our assessment procedures recognise that the aims of the curriculum are addressed through depth within a topic.

• Key learning points are identified during planning (collaboratively in year groups) and a clear journey through the maths is shown in lessons and also reflected on working walls. Questions will probe pupil understanding throughout and responses are expected in full sentences, using precise mathematical vocabulary.

• Difficult points and potential misconceptions are identified during the planning process and used as opportunities for learning. Children are then supported through these.

• Fluency – We recognise that ‘fluency’ is not just about remembering facts and aim to develop all aspects of fluency through lessons. As a school we are focusing on developing instant recall of key facts, such as number bonds, multiplication table and addition facts. Increasing fluency in basic facts allows children to free working memory and solve more complex problems.

• Split lesson - we are currently trialling 2 x 30 minute lessons in some year groups. Dividing the daily session in this way affords the optimum time to sustain children's concentration.

Lesson Structure

• Exploration - instead of ‘Let me teach you…’ as a starting point, children are encouraged to explore a problem themselves to see what they already know. At the beginning of each lesson this exploration is begun with an ‘anchor task’. Lesson objectives are not always shared with children at the beginning of the lesson because we wish the children to reason for themselves. At some point from the middle or even at the end of the lesson, the children may be asked to reflect on what they’ve been learning that day.

• Develop reasoning and deep understanding – problems are usually set in real life contexts, carefully chosen representations (manipulatives and images) are used by all to explore concepts. The use of practical resources, pictorial representations and recording takes place in every lesson following the Concrete Pictorial Abstract approach (CPA).

• Structuring - the teacher will organise the findings of the exploration, comparing and contrasting strategies to guide toward the most efficient strategy (or the one being learned that day).

• Step by step approach – developing a journey through the mathematics, steps may appear small especially at the beginning of a lesson. There are also points when suddenly a jump appears to have been made, or an extra challenge is introduced.

• Questions to challenge thinking – teachers use questioning throughout every lesson to check understanding – a variety of questions are used to foster different levels of thinking e.g.  How do you know? Can you prove it? Are you sure? Is that right? What’s the same/different about? Can you explain that? What does your partner think? Can you imagine? Questions are also used to further challenge children who have grasped the concept.

• Discussion and feedback – children have opportunities to talk to their partners and explain/clarify their thinking throughout the lesson. They are expected to listen to each other’s responses and may be asked to explain someone else’s ideas in their own words, or if they agree/disagree. 

• Practising - not drill and practice, but intelligent practice characterised by variation – children are expected to work independently in the final part of the lesson.

• Journaling – we are developing the use of journals to give children an opportunity to extend and deepen their understanding. This could be: evaluative – where a student makes a judgement on the efficiency of a method or explains their preferred method; descriptive – where a student explains different ways to answer a problem; investigative – where students explore if a method always works; and, creative – where students create their own problems for their friends to answer.

• Rapid intervention (same day catch up) – in mathematics lessons new learning is built upon previous understanding. In order for learning to progress and to keep the class together, areas of difficulty are dealt with as and when they occur. This is addressed through same day intervention.

• Marking – the marking policy follows the NCETM guidance published in April 2016. Children’s work is highlighted with green or pink, or marked using a green pen, and a comment will only be made if this is necessary to move learning forward. The most valuable feedback will be given immediately, during lessons.

At Stopsley we aim to nurture a Growth Mindset ethos. We have high expectations of all children and believe that everyone can achieve in mathematics. Challenge is provided through problem solving to achieve a greater depth of understanding. We also recognise that some children may need longer to grasp concepts and require careful scaffolding, or extra time and support.